On weak positive predicates over a finite set
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Svetlana N. Selezneva
Abstract
Predicates that are preserved by a semi-lattice function are considered. These predicates are called weak positive. A representation of these predicates are proposed in the form of generalized conjunctive normal forms (GCNFs). Properties of GCNFs of these predicates are obtained. Based on the properties obtained, more efficient polynomial-time algorithms are proposed for solving the generalized satisfiability problem in the case when all initial predicates are preserved by a certain semi-lattice function.
Note: Originally published in Diskretnaya Matematika (2018) 30, №3, 127–140 (in Russian).
Acknowledgment
The author is grateful to Prof. V. B. Alekseev for discussion of the work and several valuable remarks.
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Funding: The work is supported by Russian Foundation on Basic Research, project no. 17–01–00782-a.
References
[1] Jeavons P., Cohen D., Cooper M., “Constraints, consistency and closure”, Artificial Intelligence, 101 (1-2) (1998), 251–265.10.1016/S0004-3702(98)00022-8Search in Google Scholar
[2] Jeavons P., Coher D., Gyssens M., “Closure properties of constraints”, J. ACM, 44 (1997), 527–548.10.1145/263867.263489Search in Google Scholar
[3] Bulatov A., Jeavons P., Krokhin A., “Classifying the complexity of constraints using finite algebras”, SIAM J. Comput., 34:3 (2005), 720–742.10.1137/S0097539700376676Search in Google Scholar
[4] Maroti M., Mckenzie R., “Existence theorems for weakly symmetric operations”, Algebra Universalis, 59:3-4 (2008), 463–489.10.1007/s00012-008-2122-9Search in Google Scholar
[5] Zhuk D., “An algorithm for constraint satisfaction problem”, Proc. IEEE 47th Int. Symp. Multiple-Valued Logic, 2017, 1–6.10.1109/ISMVL.2017.20Search in Google Scholar
[6] Schaefer T., “Complexity of satisfiability problems”, Proc. 10th ACM Symp. Theory of Computing, 1978, 216–226.10.1145/800133.804350Search in Google Scholar
[7] Bulatov A. A., “A dichotomy theorem for constraint satisfaction problems on a 3-element set”, J. ACM, 53:1 (2006), 66–120.10.1145/1120582.1120584Search in Google Scholar
[8] Jeavons P.J., Cooper M.C., “Tractable constraints on ordered domains”, Artificial Intelligence, 79 (1995), 327–339.10.1016/0004-3702(95)00107-7Search in Google Scholar
[9] Bulatov A.A., “The property of being polynomial for Mal’tsev constraint satisfaction problems”, Algebra and Logic, 45:6 (2006), 371–388.10.1007/s10469-006-0035-2Search in Google Scholar
[10] Selezneva S. N., “On bijunctive predicates over a finite set”, Discrete Math. Appl., 29:1 (2019), 49–58.10.1515/dma-2019-0006Search in Google Scholar
[11] Yablonskiy S. V., “Functional constructions in fc-valued logic”, Trudy Mat. Inst. Steklov., Acad. Sci. USSR, 51, M.: MAKS Press, 2004, 5–142 (in Russian).Search in Google Scholar
[12] Dechter R., “From local to global consistency”, Artificial Intelligence, 55 (1992), 87–107.10.1016/0004-3702(92)90043-WSearch in Google Scholar
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